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Computing with Infinite Objects: the Gray Code Case [PDF]
Logical Methods in Computer Science, 2023 Infinite Gray code has been introduced by Tsuiki as a redundancy-free representation of the reals. In applications the signed digit representation is mostly used which has maximal redundancy.
Dieter Spreen, Ulrich Berger
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Axiomatization of betweenness in order-theoretic trees [PDF]
Logical Methods in Computer Science, 2021 The ternary betweenness relation of a tree, B(x,y,z) expresses that y is on the unique path between x and z. This notion can be extended to order-theoretic trees defined as partial orders such that the set of nodes larger than any node is linearly ...
Bruno Courcelle
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Convexity via Weak Distributive Laws [PDF]
Logical Methods in Computer Science, 2022 We study the canonical weak distributive law $\delta$ of the powerset monad over the semimodule monad for a certain class of semirings containing, in particular, positive semifields.
Filippo Bonchi, Alessio Santamaria
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Overlap Algebras: a Constructive Look at Complete Boolean Algebras [PDF]
Logical Methods in Computer Science, 2020 The notion of a complete Boolean algebra, although completely legitimate in constructive mathematics, fails to capture some natural structures such as the lattice of subsets of a given set.
Francesco Ciraulo, Michele Contente
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Canonicity and homotopy canonicity for cubical type theory [PDF]
Logical Methods in Computer Science, 2022 Cubical type theory provides a constructive justification of homotopy type theory. A crucial ingredient of cubical type theory is a path lifting operation which is explained computationally by induction on the type involving several non-canonical choices.
Thierry Coquand +2 more
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Reachability for infinite time Turing machines with long tapes [PDF]
Logical Methods in Computer Science, 2020 Infinite time Turing machine models with tape length $\alpha$, denoted $T_\alpha$, strengthen the machines of Hamkins and Kidder [HL00] with tape length $\omega$. A new phenomenon is that for some countable ordinals $\alpha$, some cells cannot be halting
Merlin Carl +2 more
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Dynamic Cantor Derivative Logic [PDF]
Logical Methods in Computer Science, 2023 Topological semantics for modal logic based on the Cantor derivative operator gives rise to derivative logics, also referred to as $d$-logics. Unlike logics based on the topological closure operator, $d$-logics have not previously been studied in the ...
David Fernández-Duque, Yoàv Montacute
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Approximation systems for functions in topological and in metric spaces [PDF]
Logical Methods in Computer Science, 2013 A notable feature of the TTE approach to computability is the representation of the argument values and the corresponding function values by means of infinitistic names.
Dimiter Skordev
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On Small Types in Univalent Foundations [PDF]
Logical Methods in Computer Science, 2023 We investigate predicative aspects of constructive univalent foundations. By predicative and constructive, we respectively mean that we do not assume Voevodsky's propositional resizing axioms or excluded middle.
Tom de Jong, Martín Hötzel Escardó
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Compact manifolds with computable boundaries [PDF]
Logical Methods in Computer Science, 2013 We investigate conditions under which a co-computably enumerable closed set in a computable metric space is computable and prove that in each locally computable computable metric space each co-computably enumerable compact manifold with computable ...
Zvonko Iljazovic
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